The geometric genus of splice-quotient singularities
Algebraic Geometry
2025-12-16 v2
Abstract
We prove a formula for the geometric genus of splice-quotient singularities (in the sense of Neumann and Wahl). This formula enables us to compute the invariant from the resolution graph; in fact, it reduces the computation to that for splice-quotient singularities with smaller resolution graphs. We also discuss the dimension of the first cohomology groups of certain invertible sheaves on a resolution of a splice-quotient singularity.
Keywords
Cite
@article{arxiv.math/0610464,
title = {The geometric genus of splice-quotient singularities},
author = {Tomohiro Okuma},
journal= {arXiv preprint arXiv:math/0610464},
year = {2025}
}
Comments
Two examples have been added. 17 pages. To appear in Trans. Amer. Math. Soc